In philosophy, the term anti-realism is used to describe any
position involving either the denial of the objective reality of entities of a certain type or the insistence that we should be agnostic about their real existence. Thus, we may speak of anti-realism with respect to other minds, the past, the future, universals, mathematical entities (such as natural numbers), moral categories, the material world, or even thought.

According to intuitionists (anti-realists with respect to mathematical objects), the truth of a mathematical statement consists in our ability to prove it. According to platonists (realists), the truth of a statement consists in its correspondence to objective reality. Thus, intuitionists are ready to accept a statement of the form "P or Q" as true only if we can prove P or if we can prove Q:
this is called the disjunction property. In particular, we cannot in general claim that "P or not P" is true (the law of the excluded middle), since in some cases we may not be able either to prove nor disprove the statement P. Similarly, intuitionistists object to the failure of the existence property for classical logic, where one can prove , without being able to produce any term of which holds.

Dummett argues that the intuitionistic notion of truth lies at the
bottom of various classical forms of anti-realism. He uses this
notion to re-interpret phenomenalism, claiming that it need not
take the form of a reductionism (often considered untenable).

In philosophy of science, anti-realism applies chiefly to claims about the non-reality of "unobservable" entities such as electrons, which are not detectable with our normal human senses but which many nonetheless claim are real. For a brief discussion comparing such anti-realism to its opposite, realism, see (Okasha 2002, ch. 4). Ian Hacking (1999, p. 84) also uses the same definition. The anti-realist position in the philosophy of science is often called Instrumentalism, which takes a purely functionalist view of the existence of unobservable (or only indirectly observable) entities: X exists only to the same extent that it works within a theory Y, and nothing more useful may be said about it ontologically.

In discussions of art (including visual art, writing, music, and lyrics), anti-realism and anti-realist may be used in one of the philosophical senses described above, or may simply be used in contrast to realism, in whatever sense the latter is meant. Thus surrealism in visual art is an "anti-realist" tendency, and the psychedelic bands common in the United States in the 1960s were "anti-realist," etc. These terms may not be as precise when applied to art as when applied to philosophical matters. Anti-reality is occasionally used in this sense, although it may be used in other senses.